36/5:(-5/6)^-1+sqrt{27/16}-1/8-frac{13}{4}= eching

$$\frac { 36 } { 5 } : ( - \frac { 5 } { 6 } ) ^ { - 1 } + \sqrt { \frac { 27 } { 16 } } - \frac { 1 } { 8 } - \frac { 13 } { 4 } =$$

Baholash

$$\frac{3\sqrt{3}}{4}-\frac{75}{8}\approx -8,075961894$$

Qisqa yechim qadamlari

-1 daraja ko‘rsatkichini -\frac{5}{6} ga hisoblang va -\frac{6}{5} ni qiymatni oling.

$$\frac{\frac{36}{5}}{-\frac{6}{5}}+\sqrt{\frac{27}{16}}-\frac{1}{8}-\frac{13}{4}$$

\frac{36}{5} ni -\frac{6}{5} ga bo'lish \frac{36}{5} ga k'paytirish -\frac{6}{5} ga qaytarish.

$$\frac{36}{5}\left(-\frac{5}{6}\right)+\sqrt{\frac{27}{16}}-\frac{1}{8}-\frac{13}{4}$$

-6 hosil qilish uchun \frac{36}{5} va -\frac{5}{6} ni ko'paytirish.

$$-6+\sqrt{\frac{27}{16}}-\frac{1}{8}-\frac{13}{4}$$

\sqrt{\frac{27}{16}} boʻlinmasining kvadrat ildizini \frac{\sqrt{27}}{\sqrt{16}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$-6+\frac{\sqrt{27}}{\sqrt{16}}-\frac{1}{8}-\frac{13}{4}$$

Faktor: 27=3^{2}\times 3. \sqrt{3^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$-6+\frac{3\sqrt{3}}{\sqrt{16}}-\frac{1}{8}-\frac{13}{4}$$

16 ning kvadrat ildizini hisoblab, 4 natijaga ega bo‘ling.

$$-6+\frac{3\sqrt{3}}{4}-\frac{1}{8}-\frac{13}{4}$$

-\frac{49}{8} olish uchun -6 dan \frac{1}{8} ni ayirish.

$$-\frac{49}{8}+\frac{3\sqrt{3}}{4}-\frac{13}{4}$$

-\frac{75}{8} olish uchun -\frac{49}{8} dan \frac{13}{4} ni ayirish.

$$-\frac{75}{8}+\frac{3\sqrt{3}}{4}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 8 va 4 ning eng kichik umumiy karralisi 8. \frac{3\sqrt{3}}{4} ni \frac{2}{2} marotabaga ko'paytirish.

$$-\frac{75}{8}+\frac{2\times 3\sqrt{3}}{8}$$

-\frac{75}{8} va \frac{2\times 3\sqrt{3}}{8} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{-75+2\times 3\sqrt{3}}{8}$$

-75+2\times 3\sqrt{3} ichidagi ko‘paytirishlarni bajaring.

$$\frac{-75+6\sqrt{3}}{8}$$

Omil

$$\frac{3 {(2 \sqrt{3} - 25)}}{8} = -8,075961894323342$$